Question: Enzo is studying the black bear population at a large national park. He finds that the relationship between the elapsed time $t$, in years, since the beginning of the study, and the black bear population $B(t)$, in the park is modeled by the following function. $B(t)=2500 \cdot 2^{0.01t}$ According to the model, what will the black bear population be at that national park in $25$ years? Round your answer, if necessary, to the nearest whole number.
Thinking about the problem We want to find the park's black bear population in $25$ years. In other words, we are given a $t$ value of $25$ years and want to find the bear population associated with that input, or $B(25)$. To do this, we can substitute ${25}$ in for $ t$ and evaluate. $B({25})=2500 \cdot 2^{0.01({25})}$ Evaluating the expression We can use a calculator to evaluate the expression. The answer is shown below. $\begin{aligned}B(25)&=2500\cdot 2^{{0.01(25)}}\\\\ &=2500\cdot 2^{{0.25}}\\\\ &\approx2973\\\\ \end{aligned}$ In $25$ years, the population of black bears at the park will be about $2973$ bears.